Thermodynamic studies of physisorption using the Langmuir adsorption model

Abstract

The simplest possible physical models of adsorption were developed by Irving Langmuir and provides a foundational framework for understanding gas adsorption on adsorbent surfaces. These models are extensively used to fit adsorption equilibria (experimental and computational) in order to discover thermodynamic and physical properties of the adsorption system. Even with the simplest variant, the single-site Langmuir model, these models can accurately describe a vast range of different adsorbate gases and adsorbents, but there is still the question of how meaningful the resulting physical and thermodynamic properties are. The Langmuir models can be elegantly derived using first-principles statistical mechanics where one can account for the individual degrees of freedom in the adsorbed phase. As the gas adsorbate transitions from the free bulk phase to the adsorbed phase at a binding site, it can have different degrees of freedom, leading to different temperature dependencies of the Langmuir constant. To assess which description is experimentally validated, we measured hydrogen adsorption equilibria on [Ni 3(pzdc) 2(ade) 2(H 2O) 4] and fit them to a wide array of single-site Langmuir models. Interestingly, all of the models were found to be validated, but the average temperature isosteric enthalpy of adsorption was determined to be a reliable common metric among them. In a second study, methane adsorption was measured on MOF-5, a more complicated system with four different binding sites spanning a wide range of binding energies. In this work, we fit the measured adsorption equilibria to a wide array of multi-site Langmuir models to determine the binding energy of the four different binding sites using only experimental methane adsorption equilibria. These results show the important limits of this method, especially at supercritical conditions. Lastly, methane adsorption was measured on a set of five model porous carbons to determine the effects of confinement and binding site environments on the isosteric enthalpy of adsorption. The comparison between zeolite-templated carbon and graphene mesosponge is emphasized, highlighting that the increasing isosteric enthalpy of adsorption in zeolite templated carbon is due to uniform confinement and the presence of three-ring binding sites.